How are we aware of our surroundings? Somehow, from a pair of tiny, two-dimensional pictures of the visual world – provided by our retinas – our brains are able to render the world as it is, accurately depicting the locations of both a distant mountain range and the camera we are pointing at it. To understand how space is represented in the brain, neurophysiologists have borrowed the useful concept of a reference frame (also called a coordinate frame) from engineers and physicists. A reference frame, in the mathematical sense, is simply a set of rigid axes that intersect at a point, the origin. These axes are usually perpendicular to each other, and they are marked with gradations. This system allows the location of any object to be described by a set of numbers, called coordinates – its position along each of the axes. How is this notion useful in neuroscience? It allows us to phrase questions about how the brain encodes space in very concrete terms. For example, suppose we wish to understand how it is that a person can catch a baseball. Using reference frames, we can state the question as, ‘How does the brain translate the position of the ball from the coordinates of the retinas into its coordinates in a reference frame centered on the left hand?’ (Figure 1) Some modifications to the physicist’s concep of a reference frame are needed to apply it in neuroscience. Neurons in the visual system do not report the coordinates of an object. Instead, neurons that encode visual space each represent a very restricted region of space. Cells will respond to stimuli located in one particular location, termed the response field of the neuron, or the receptive field in cases where the neuron’s response is considered to be strictly sensory, and will not respond to the same object positioned somewhere else. (Often, a visual stimulus must have other features in order for a neuron to respond to it, such as a particular color, a direction in which it is moving, or even how the animal intends to respond to that stimulus.) Areas of the brain that represent visual space do so by using a population of neurons with response fields at different locations. Once we locate the response field for a neuron, we can ask in which reference frame that neuron encodes space using some very simple manipulations: by moving one part of the body at a time, we can explore whether the neuron’s response field moves along with that body part. If it does, then we have reason to believe that the neuron encodes space in a reference frame anchored to that body part.